Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A geometric perspective on p-adic properties of mock modular forms

A geometric perspective on p-adic properties of mock modular forms Bringmann et al. (Trans Am Math Soc 364(5):2393–2410, 2012) showed how to ‘regularize’ mock modular forms by a certain linear combination of the Eichler integral of their shadows in order to obtain p-adic modular forms in the sense of Serre. In this paper, we give a new proof of a refined form of their results (for good primes p) by employing the geometric theory of harmonic Maass forms developed by Candelori (Math Ann 360(1–2):489–517, 2014) and the theory of overconvergent modular forms due to Katz and Coleman. In particular, our main results imply that the p-adic modular forms in Bringmann et al. (2012) are overconvergent. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

A geometric perspective on p-adic properties of mock modular forms

Loading next page...
 
/lp/springer-journals/a-geometric-perspective-on-p-adic-properties-of-mock-modular-forms-mCGbQrxrgm

References (9)

Publisher
Springer Journals
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
DOI
10.1186/s40687-017-0095-z
Publisher site
See Article on Publisher Site

Abstract

Bringmann et al. (Trans Am Math Soc 364(5):2393–2410, 2012) showed how to ‘regularize’ mock modular forms by a certain linear combination of the Eichler integral of their shadows in order to obtain p-adic modular forms in the sense of Serre. In this paper, we give a new proof of a refined form of their results (for good primes p) by employing the geometric theory of harmonic Maass forms developed by Candelori (Math Ann 360(1–2):489–517, 2014) and the theory of overconvergent modular forms due to Katz and Coleman. In particular, our main results imply that the p-adic modular forms in Bringmann et al. (2012) are overconvergent.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Mar 3, 2017

There are no references for this article.